我在一些地方修改了你的代码：
1-将行内容放在变量中以提高可读性
2-更正了填充每行<select>的方式。
而且很有效

// fake values for dropdown only for testing
var dropdownOptions = [{
    Text: "a",
    Value: "1"
  },
  {
    Text: "b",
    Value: "2"
  },
  {
    Text: "c",
    Value: "3"
  }
];

var counter = 1;

$(function() {

  $("#add").click(function() {
    // create a row, add content to it and append to table
    $('<tr id="tableRow' + counter +'">' + rowContent + "</tr>").appendTo("#submissionTable");

    counter++;
    return false;
  });
});

// content of each row
var rowContent = "<td>" +
  '<label id="CountItems"><strong>' +
  counter +
  "</strong></label>" +
  "</td>" +
  '<td width="40%">' +
  '<select onchange="sendInfo(this)" class="form-select js-dropdown" name="Item_Id[' +
  counter +
  ']" id="ItemId"' + counter + 'required="required"> ' + populate() +
  "</select>" +
  "</td>" +
  '<td width="10%">' +
  '<input type="text" class="form-control" name="Qty[' +
  counter +
  ']" value="1" id="Qty"' + counter + ' required="required" />' +
  "</td>" +
  '<td width="10%">' +
  '<input type="text" class="form-control" name="AcidStables[' +
  counter +
  ']" value="" required="required" />' +
  "</td>" +
  '<td width="20%">' +
  '<input type="text" class="form-control" name="Unit_Price[' +
  counter +
  ']" value="0.00" id="UnitPrice"' + counter + '  required="required" />' +
  "</td>" +
  '<td width="20%">' +
  '<input type="text" class="form-control" name="Line_Total[' +
  counter +
  ']" value="0.00" id="LineTotal"' + counter + ' required="required" />' +
  "</td>" +
  "<td>" +
  '<button type="button" class="btn btn-danger" onclick="removeTr(' +
  counter +
  ');">x</button>' +
  "</td>";

//Populate the <select> element with options
// this function is called inside the rowContent variable above 
function populate() {
  var options = "";
  dropdownOptions.forEach(function(option) {

    options += $("<option>").val(option.Value).text(option.Text).get(0).outerHTML;

  });
  return options;
}

// this function is set for onchange event of <select> inside the rowContent variable above
function sendInfo(e) {
  console.log(e.name, e.value);
  console.log(e.closest("tr").id);
  // todo: send data to wherever is needed
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>

<button type="button" id="add">Add</button>
<table id="submissionTable">

</table>

更新

对不起，我似乎忘记了原始答案中的行id。
那么，要获取row.id，您可以使用element.closest()函数。
我更新了我的代码片段如下：
1-给每一行一个id（就像你在问题中做的那样）：
$('<tr id="tablerow' + counter +'">' + rowContent + "</tr>").appendTo("#submissionTable");
2-使用row.idclosest()在sendInfo()函数中检索www.example.com：
console.log(e.closest("tr").id);